From the Bethe Ansatz to the Gessel-Viennot theorem. Submitted to Annals of Comb

Abstract. We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalized inhomogeneous, five-vertex model on the square lattice, given certain conditions hold, is equivalent to the Gessel–Viennot determinant for the number of configurations of N non-intersecting directed lattice paths, or vi-cious walkers, with various boundary conditions. Our theorems are sufficiently general to allow generalisation to any regular planar lattice